Open Timelike Curves Violate Heisenberg’s Uncertainty Principle

Abstract

Toy models for quantum evolution in the presence of closed timelike curves (CTCs) have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require non-trivial interactions between the future and past which lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the CTC, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave-packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time-dilation suggests that OTCs provide a novel alternative to existing proposals for the behaviour of quantum systems under gravity.

Replicating the benefits of Deutschian closed timelike curves without breaking causality

“…In cases where the input state is deterministically prepared in a pure state, shot-by-shot, but the particular state may change shotby-shot, there remains some ambiguity. The conventional view is taken by Bacon, 10 Brun et al 6 and Pienaar et al 13 -that subensembles of identical input states should be treated as pure. Others argue that if this sequence is truly random, then the randomness must always be treated as if it arose from the purification of an entangled quantum state.…”

“…In this context, Pienaar et al considered a special case of Deutschian CTCs known as open timelike curves 13 (OTCs). Consider a particle that travels back in time with respect to a chronology-respecting observer, but is completely isolated from anything that can affect its own causal past during the time-traveling process (See Figure 1).…”

“…This drastically improves the potential of harnessing such power via alternative effects-such as certain models of gravitational time dilation. 13 Thus, we open the possibility of testing the many radical protocols that harness CTCs in significantly less controversial settings.…”

Quantum State Cloning Using Deutschian Closed Timelike Curves

“…The possible existence of closed timelike curves (CTCs) in certain exotic spacetime geometries [1][2][3] has sparked a significant amount of research regarding their ramifications for computation [4][5][6] and information processing [7,8]. One of the well known models for CTCs is due to Deutsch [9], who had the insight to abstract away much of the space-time geometric details and use the tools of quantum information to address physical questions about causality paradoxes.…”

“…Furthermore, our results show that Deutsch's model for CTCs is in fact a classical model, in the sense that two arbitrary, distinct density operators are perfectly distinguishable (in the limit of a large CTC system); hence, in this model quantum mechanics becomes a classical theory in which each density operator is a distinct point in a classical phase space. The possible existence of closed timelike curves (CTCs) in certain exotic spacetime geometries [1][2][3] has sparked a significant amount of research regarding their ramifications for computation [4][5][6] and information processing [7,8]. One of the well known models for CTCs is due to Deutsch [9], who had the insight to abstract away much of the space-time geometric details and use the tools of quantum information to address physical questions about causality paradoxes.…”